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Nash Equilibria on (Un)Stable Networks

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  • Anton Badev

Abstract

In response to a change, individuals may choose to follow the responses of their friends or, alternatively, to change their friends. To model these decisions, consider a game where players choose their behaviors and friendships. In equilibrium, players internalize the need for consensus in forming friendships and choose their optimal strategies on subsets of k players—a form of bounded rationality. The k‐player consensual dynamic delivers a probabilistic ranking of a game's equilibria, and via a varying k, facilitates estimation of such games. Applying the model to adolescents' smoking suggests that: (a) the response of the friendship network to changes in tobacco price amplifies the intended effect of price changes on smoking, (b) racial desegregation of high schools decreases the overall smoking prevalence, (c) peer effect complementarities are substantially stronger between smokers compared to between nonsmokers.

Suggested Citation

  • Anton Badev, 2021. "Nash Equilibria on (Un)Stable Networks," Econometrica, Econometric Society, vol. 89(3), pages 1179-1206, May.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:3:p:1179-1206
    DOI: 10.3982/ECTA12576
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    References listed on IDEAS

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    Cited by:

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    2. Ugo Bolletta & Paolo Pin, 2024. "Dynamic opinion updating with endogenous networks," Papers 2405.01341, arXiv.org.
    3. Gaonkar, Shweta & Mele, Angelo, 2023. "A model of inter-organizational network formation," Journal of Economic Behavior & Organization, Elsevier, vol. 214(C), pages 82-104.
    4. Mathieu Lambotte & Sandrine Mathy & Anna Risch & Carole Treibich, 2022. "Spreading active transportation: peer effects and key players in the workplace," Post-Print hal-03702684, HAL.
    5. Charroin, Liza & Fortin, Bernard & Villeval, Marie Claire, 2022. "Peer effects, self-selection and dishonesty," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 618-637.
    6. Liza Charroin & Bernard Fortin & Marie Claire Villeval, 2022. "Peer effects, self-selection and dishonesty," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03712450, HAL.
    7. Lambotte, Mathieu & Mathy, Sandrine & Risch, Anna & Treibich, Carole, 2023. "Disentangling peer effects in transportation mode choice: The example of active commuting," Journal of Environmental Economics and Management, Elsevier, vol. 121(C).
    8. Lin, Zhongjian & Hu, Yingyao, 2024. "Binary choice with misclassification and social interactions, with an application to peer effects in attitude," Journal of Econometrics, Elsevier, vol. 238(1).
    9. Bolletta, Ugo, 2021. "A model of peer effects in school," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 1-10.
    10. Candelaria, Luis E. & Ura, Takuya, 2023. "Identification and inference of network formation games with misclassified links," Journal of Econometrics, Elsevier, vol. 235(2), pages 862-891.
    11. Liza Charroin & Bernard Fortin & Marie Claire Villeval, 2022. "Peer effects, self-selection and dishonesty," Post-Print hal-03712450, HAL.
    12. Golub, Benjamin & Hsieh, Yu-Chi & Sadler, Evan, 2024. "On the difficulty of characterizing network formation with endogenous behavior," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 107-110.
    13. Christis Katsouris, 2024. "Robust Estimation in Network Vector Autoregression with Nonstationary Regressors," Papers 2401.04050, arXiv.org.
    14. Alan Griffith, 2022. "A continuous model of strong and weak ties," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(6), pages 1519-1563, December.
    15. Benjamin Golub & Yu-Chi Hsieh & Evan Sadler, 2023. "On the Difficulty of Characterizing Network Formation with Endogenous Behavior," Papers 2302.05831, arXiv.org, revised Feb 2023.

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